Photonic production of B_c-mesons

The cross section of the $\gamma \gamma \rightarrow B_c(B_c^*) \bar b c$ process is calculated. It is shown that near threshold the pseudoscalar state production is much suppressed with respect to the vector one. At large energies their ratio becaims $\sigma(B_c^*)/sigma(B_c)\sim 4$. The process of heavy quark recombination dominates in the production of $B_c(B_c^*)$ states. The fragmentation process $b\to B_c$ comes to play at high $p_t$ values only, while its contribution will remain nondominant.Comment: Preprint IHEP 94-8

f_B^{stat} and \mu_\pi^2 in quasiclassical approximation of sum rules

In the framework of sum rules with a use of quarkonium mass spectrum, evaluated in the quasiclassical approximation, estimates of leptonic constant $f_B^{stat}\simeq 320\pm 60$ MeV in a static limit and for the average heavy quark momentum squared $\mu_\pi^2 \simeq 0.5\pm 0.1$ GeV$^2$ are obtained.Comment: 7 pages, LATEX fil

Absolutely continuous spectrum of perturbed Stark operators

We prove new results on the stability of the absolutely continuous spectrum for perturbed Stark operators with decaying or satisfying certain smoothness assumption perturbation. We show that the absolutely continuous spectrum of the Stark operator is stable if the perturbing potential decays at the rate $(1+x)^{-\frac{1}{3}-\epsilon}$ or if it is continuously differentiable with derivative from the H\"older space $C_{\alpha}(R),$ with any $\alpha>0.

Regularity and blow up for active scalars

We review some recent results for a class of fluid mechanics equations called active scalars, with fractional dissipation. Our main examples are the surface quasi-geostrophic equation, the Burgers equation, and the Cordoba-Cordoba-Fontelos model. We discuss nonlocal maximum principle methods which allow to prove existence of global regular solutions for the critical dissipation. We also recall what is known about the possibility of finite time blow up in the supercritical regime.Comment: 33 page